CN113050417A - Design method of rapid finite time controller of all-state constraint mechanical arm - Google Patents

Design method of rapid finite time controller of all-state constraint mechanical arm Download PDF

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CN113050417A
CN113050417A CN202110218029.7A CN202110218029A CN113050417A CN 113050417 A CN113050417 A CN 113050417A CN 202110218029 A CN202110218029 A CN 202110218029A CN 113050417 A CN113050417 A CN 113050417A
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mechanical arm
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陈响
郑世祺
陈扬孜
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China University of Geosciences
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Abstract

The invention provides a design method of a rapid finite time controller of a full-state constraint mechanical arm, which comprises the following steps: designing an observer, specifically: establishing a mechanical arm system kinetic equation; establishing an initial state equation of the mechanical arm system; designing a finite time disturbance observer; establishing a state equation of the mechanical arm system; and designing the mechanical arm controller based on a backstepping method. The controller designed by the method provided by the invention can ensure that the mechanical arm system is fast and stable in limited time, the output of the mechanical arm system can well follow the change of a given signal, and the controller well solves the problem of fast limited time tracking control of the mechanical arm system under the condition of meeting the constraint condition.

Description

Design method of rapid finite time controller of all-state constraint mechanical arm
Technical Field
The invention relates to the technical field of mechanical arm design, in particular to a design method of a rapid finite time controller of an all-state constraint mechanical arm.
Background
With the rapid development of the fields of communication, computer, network, etc., the related issues of the robot arm have become a new research direction in the field of automatic control. The mechanical arm can participate in completing work in various complex environments, so that the position of the mechanical arm in industrial production and social life is continuously improved. Therefore, in order to better utilize the mechanical arm to assist in completing various tasks, the control problem of the mechanical arm is receiving more and more attention from researchers.
Since the robot arm system is a typical nonlinear system, the design method of such a nonlinear system controller is to first formulate the robot arm dynamics into a linear equation by feedback linearization, and then design the controller by using the linear system technology. However, for the mechanical arm, the feedback linearization method cannot sufficiently acquire the dynamic characteristics of the nonlinear system in the design process of the controller, so that the tracking error is difficult to eliminate. In order to design a controller to bring the robotic arm to a precise specified position or to track a predetermined path, many researchers have introduced a differential geometry approach for controlling it. Aiming at the control problem of a general mechanical arm, some researchers provide a backstepping design-based self-adaptive output feedback controller; still others have implemented robust control of the robotic arm using simple PD control and H ∞ control. However, a common feature of these methods is that once the controller is determined, it cannot adjust in time according to the output of the nonlinear system in the control process, and cannot sufficiently acquire the dynamics of the nonlinear system, so that a tracking error is necessarily generated. With the further development of the nonlinear system control method, sliding mode variable structure control is applied to the control problem of the mechanical arm as a typical nonlinear control method. It can make the control system have strong robustness in the situation of change and external disturbance. In recent years, a method of intelligent control is further developed, and compared with a traditional control method, a neural network control and fuzzy control method are proved to be capable of well processing an uncertain nonlinear system, and the method has excellent nonlinear fitting capability and high adaptability. Therefore, intelligent control methods for the mechanical arm are emerging continuously, so that the control theory of the mechanical arm is more and more mature.
Although much control results about the robot arm are obtained, no relevant research results are obtained in the aspect of adaptive rapid finite time control of the all-state constraint robot arm. On one hand, in practical application, the control system is subjected to various constraints, such as angle constraint, moment constraint and the like; on the other hand, due to the rapid development of industrial production, higher industrial production indexes and higher safety requirements force rapid limited time control to be a necessary consideration. Although related researches relate to the control problem of the mechanical arm under the full-state constraint, no related researches relate to the adaptive rapid limited-time control under the full-state constraint, and therefore the control performance of the mechanical arm has partial defects. Firstly, in the aspect of control precision, the existing control method has a large tracking error during tracking control, and cannot ensure that a system outputs a precise tracking reference signal; secondly, in terms of time, the control time of the existing control method for the mechanical arm is relatively long, which cannot meet higher control requirements.
Therefore, the adaptive fast finite time control research of the full-state constraint mechanical arm system still faces a lot of challenges, and two problems to be solved exist mainly: firstly, for system constraint, how to design a barrier Lyapunov function meeting constraint conditions; and secondly, how to design a fast finite time controller based on the unknown external disturbance influence.
Disclosure of Invention
In view of the above, the present invention provides a design method of a fast finite time controller of a full-state constraint robot arm.
The invention provides a design method of a rapid finite time controller of a full-state constraint mechanical arm, which comprises the following steps:
s1, designing an observer, specifically: establishing a mechanical arm system kinetic equation; establishing an initial state equation of the mechanical arm system; designing a finite time disturbance observer; establishing a state equation of the mechanical arm system;
and S2, designing the mechanical arm controller based on the backstepping method.
Further, in step S1, the specific steps of designing the observer are:
s1.1, establishing a mechanical arm system kinetic equation:
Figure BDA0002954683140000031
wherein, q is the angular position,
Figure BDA0002954683140000032
is angular acceleration, M is moment of inertia, M isThe mass of the connecting rod, g is the acceleration of gravity, F is the acting force, and l is the length of the connecting rod;
s1.2, establishing an initial state equation of the mechanical arm system:
the state variables and the control input quantities of the mechanical arm system are defined as follows:
Figure BDA0002954683140000033
wherein x is1、x2Is a state variable of the arm system, u is a control input amount of the arm system,
Figure BDA0002954683140000034
is the angular velocity;
the mechanical arm system dynamics equation (1) is expressed as:
Figure BDA0002954683140000035
wherein d is1And d2Respectively, external disturbance, assuming external disturbance di(i ═ 1,2) is bounded, and their derivatives are bounded; phi1＝0,Φ2(x1)＝-0.5mglsin(x1)；
S1.3, designing a finite time disturbance observer:
Figure BDA0002954683140000041
wherein v is0i，v1i，v2iAre respectively intermediate variables, L1、L2、L3To observe the coefficient, λ0,λ1,λ2Respectively, of a finite-time disturbance observer, σ0i,σ1i,σ2iAre respectively
Figure BDA0002954683140000042
The observed value of (a); finally, sigma can be realized1i＝diThus, the observation of external disturbance can be realized; the mechanical arm system can be subjected to unknown external disturbance, so that a system model contains an uncertain item, the control performance of the system model is influenced, the disturbance observer can well observe the external disturbance, the influence of the external disturbance on the mechanical arm system can be better weakened, and the control performance of the mechanical arm system is improved;
s1.4, establishing a state equation of the mechanical arm system:
definition of diObserved value of
Figure BDA0002954683140000043
The initial state equation (3) of the mechanical arm system is expressed as:
Figure BDA0002954683140000044
further, in step S2, the specific steps of designing the manipulator controller based on the back stepping method are as follows:
s2.1, selecting a Lyapunov function V meeting constraint conditions based on a barrier exponentiation integral technology1：
Figure BDA0002954683140000045
Wherein ξ1Is the tracking error, ξ1＝x1－yd，ydIs a reference signal, η1(t) is a symmetric time-varying constraint function,
Figure BDA0002954683140000046
η11,η12respectively, constant, t time, τ1Is a time constant; the Lyapunov function can ensure that the state of the mechanical arm system does not violate the constraint condition in the whole process; the constraint conditions are set according to actual needs;
s2.2, for Lyapunov function V1Calculating the first derivative, simplifying, and selecting proper virtual control law alpha1：
Figure BDA0002954683140000051
Wherein, iota1,ι2,r2To a selected constant, r2δ is a fraction where both the numerator and denominator are odd and 1/2<δ<1；
Figure BDA0002954683140000052
Is d1The observed value of (a); virtual control law alpha1Enabling state variables x of the arm system1The requirement of fast finite time tracking reference signals is met;
s2.3, the design of the virtual control law is combined, and the Lyapunov function V can be guaranteed1Derivative of (2)
Figure BDA0002954683140000053
Wherein a and b respectively represent constants, a is more than 0, and b is more than 0;
s2.4, introducing coordinate transformation:
Figure BDA0002954683140000054
s2.5, selecting a proper Lyapunov function V2：
Figure BDA0002954683140000055
Wherein the content of the first and second substances,
Figure BDA0002954683140000056
s is an argument of the function v(s), η2(t) is a time-varying constraint function,
Figure BDA0002954683140000057
η21,η22respectively, constant, t time, τ2Is a time constant;
s2.6, for Lyapunov function V2Derivation and combinationBriefly, during the design process, fuzzy logic is selected for unknown non-linear functions
Figure BDA0002954683140000058
Performing approximate estimation, non-linear function
Figure BDA0002954683140000059
The expression of (a) is:
Figure BDA00029546831400000510
wherein θ ═ θ1,θ2…,θN]TIs a weight vector, S (x) S1(x),S2(x),…SN(x)]TAnd is and
Figure BDA00029546831400000511
1,2, …, N; wherein k is 1,2, …, N, j is 1,2, …, N, N and N are all natural numbers greater than 1,
Figure BDA00029546831400000512
generally selected as a gaussian relationship function;
s2.7, for non-linear functions
Figure BDA00029546831400000513
Making an identity change to obtain an expression:
y(x)＝θ*TS(x)+ε(x) (12)
wherein, theta*And ε (x) is the ideal optimal weight and the approximation error under that optimal weight, respectively;
s2.8, using expressions (11) and (12) to apply fuzzy logic to nonlinear function in design process
Figure BDA0002954683140000065
Performing approximation processing, thereby designing a control input u of the mechanical arm system, namely a fuzzy virtual control law:
Figure BDA0002954683140000061
wherein, iota3,ι4,r3K is a selected constant;
Figure BDA0002954683140000062
is d2The observed value of (a);
Figure BDA0002954683140000063
s2.9, the design of the fuzzy virtual control law can ensure the Lyapunov function V2Derivative of (2)
Figure BDA0002954683140000064
Wherein c and d respectively represent constants, c is more than 0, and d is more than 0.
The invention also provides a mechanical arm system which comprises a controller, wherein the controller is obtained by the design method.
The design method provided by the invention aims at the all-state constraint mechanical arm system containing unknown disturbance, based on the power integration technology, the constraint condition is not violated, the observation compensation is carried out on the external disturbance by introducing the finite time disturbance observer, the backstepping design method and the fuzzy logic are adopted to carry out approximate fitting on the nonlinear item, so that the fuzzy rapid finite time controller is designed, the precise tracking of the mechanical arm system on the reference signal is realized, and the stability of the whole closed-loop system is ensured. Therefore, the design method provided by the invention can ensure the accurate tracking control of the all-state constraint mechanical arm system, and can also shorten the control time and improve the response rate of the system.
The controller designed by the method provided by the invention can ensure that the mechanical arm system is fast and stable in limited time, the output of the mechanical arm system can well follow the change of a given signal, and the controller well solves the problem of fast and limited time tracking control of the mechanical arm system under the condition of meeting the constraint condition.
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FIG. 1 is a flow chart of a method for designing a fast finite time controller for a full-state constraint robot.
Fig. 2 is a simulation diagram of a disturbance observer designed in embodiment 1 of the present invention.
Fig. 3 is a simulation diagram of the control law of the controller according to embodiment 1 of the present invention.
Fig. 4 is a tracking error simulation diagram of the robot arm system according to embodiment 1 of the present invention.
Fig. 5 is a state simulation diagram of the robot arm system according to embodiment 1 of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be further described with reference to the accompanying drawings.
Example 1:
referring to fig. 1, an embodiment 1 of the present invention provides a method for designing a fast finite time controller of a full-state constraint robot arm, including the following steps:
step S1, designing an observer, specifically:
s1.1, establishing a mechanical arm system kinetic equation:
Figure BDA0002954683140000071
wherein, q is the angular position,
Figure BDA0002954683140000074
is angular acceleration, M is moment of inertia, M is link mass, g is gravitational acceleration, F is acting force, l is link length;
s1.2, establishing an initial state equation of the mechanical arm system:
the state variables and the control input quantities of the mechanical arm system are defined as follows:
Figure BDA0002954683140000072
wherein x is1、x2Is a state variable of the arm system, u is a control input amount of the arm system,
Figure BDA0002954683140000073
is the angular velocity;
the mechanical arm system dynamics equation (1) is expressed as:
Figure BDA0002954683140000081
wherein d is1And d2Respectively, external disturbance, assuming external disturbance di(i ═ 1,2) is bounded, and their derivatives are bounded; phi1＝0,Φ2(x1)＝-0.5mglsin(x1)；
S1.3, designing a finite time disturbance observer:
Figure BDA0002954683140000082
wherein v is0i，v1i，v2iAre respectively the intermediate variable, λ0,λ1,λ2Respectively, of a finite-time disturbance observer, σ0i,σ1i,σ2iAre each xi,di,
Figure BDA0002954683140000083
The observed value of (a); l is1、L2、L3Is an observation coefficient;
s1.4, establishing a state equation of the mechanical arm system:
defining an external disturbance diObserved value of
Figure BDA0002954683140000084
The initial state equation (3) of the mechanical arm system is expressed as:
Figure BDA0002954683140000085
step S2, designing the mechanical arm controller based on the backstepping method, specifically:
s2.1, selecting a Lyapunov function V meeting constraint conditions based on a barrier exponentiation integral technology1：
Figure BDA0002954683140000086
Wherein ξ1To tracking error, xi1＝x1-yd，ydIs a reference signal, η1(t) is a symmetric time-varying constraint function,
Figure BDA0002954683140000091
η11,η12respectively represent a constant, τ1Is a time constant, t represents time; the Lyapunov function can ensure that the state of the mechanical arm system does not violate the constraint condition in the whole process;
s2.2, for Lyapunov function V1Calculating the first derivative, simplifying, and selecting proper virtual control law alpha1：
Figure BDA0002954683140000092
Wherein, iota1,ι2,r2To a selected constant, r2δ is a fraction where both the numerator and denominator are odd and 1/2<δ<1；
Figure BDA0002954683140000093
Is d1The observed value of (a); virtual control quantity alpha1Enabling state x of the arm system1The requirement of fast finite time tracking reference signals is met;
s2.3, the design of the virtual control law is combined, and the Lyapunov function V can be guaranteed1Derivative of (2)
Figure BDA0002954683140000094
Wherein a and b respectively represent constants, a is more than 0, and b is more than 0;
s2.4, introducing coordinate transformation:
Figure BDA0002954683140000095
s2.5, selecting a proper Lyapunov function V2：
Figure BDA0002954683140000096
Wherein the content of the first and second substances,
Figure BDA0002954683140000097
s is an argument of the function v(s), η2(t) is a time-varying constraint function,
Figure BDA0002954683140000098
η21,η22respectively, constant, t time, τ2Is a time constant;
s2.6, for Lyapunov function V2Derivation and simplification, and in the design process, fuzzy logic pair unknown nonlinear function is selected
Figure BDA0002954683140000099
Performing approximate estimation, non-linear function
Figure BDA00029546831400000910
The expression of (a) is:
Figure BDA00029546831400000911
wherein θ ═ θ1,θ2…,θN]TIs a weight vector, S (x) S1(x),S2(x),…SN(x)]TAnd is and
Figure BDA00029546831400000912
1,2, …, N; wherein k is 1,2, …, N, j is 1,2, …, N, N and N are all natural numbers greater than 1,
Figure BDA00029546831400000913
generally selected as a gaussian relationship function;
s2.7, for non-linear functions
Figure BDA0002954683140000101
Making an identity change to obtain an expression:
y(x)＝θ*TS(x)+ε(x) (12)
wherein, theta*And ε (x) is the ideal optimal weight and the approximation error under that optimal weight, respectively;
s2.8, using expressions (11) and (12) to apply fuzzy logic to nonlinear function in design process
Figure BDA0002954683140000102
Carrying out approximation processing, thereby designing the control input quantity u of the mechanical arm system, namely a fuzzy virtual control law:
Figure BDA0002954683140000103
wherein, iota3,ι4,r3K is a selected constant;
Figure BDA0002954683140000104
is d2The observed value of (a);
Figure BDA0002954683140000105
s2.9, the design of the fuzzy virtual control law can ensure the Lyapunov function V2Derivative of (2)
Figure BDA0002954683140000106
Wherein c and d respectively represent constants, c is more than 0, and d is more than 0.
Embodiment 1 also provides a robot arm system including a controller designed using the above design method.
To verify that the controller is designed to make the robot system follow a given reference signal y for each state under the constraint of satisfying a symmetrical time-varying all-state constraintdIn the case of sin (t), example 1 uses the following parameters M1 kg, l 1M, d1＝sin(t),d22cos (t); 77/79, Lyapunov function V1The constraint conditions of (1) are set as: eta1(t)＝3e-0.5t+ 0.5; lyapunov function V2Is set to η2(t)＝3e-0.5t+ 0.5; the initial state of the arm system is set as: x is the number of1(0)＝0.8,x2(0) 0.6, the parameters of the finite time disturbance observer are set as: lambda [ alpha ]0＝3,λ1＝1.5,λ2＝1.1，L1＝L2＝L33; the gaussian relationship function in fuzzy logic is chosen as:
Figure BDA0002954683140000107
k is 1,2, … 5, where xiRepresenting an input vector; the relevant parameters of the fuzzy virtual control law u and the controller are set as follows: iota (iota) type1＝3，ι2＝2，ι3＝5,ι44, K-3, | θ | | 1; MATLAB simulation is carried out according to the set parameters, constraint conditions and initial states, a simulation graph of a disturbance observer is shown in figure 2, a simulation graph of a control law u is shown in figure 3, and as can be seen from figure 2, the finite-time disturbance observer can well observe external disturbance suffered by the mechanical arm system.
The simulation diagram of the tracking error of the mechanical arm system is shown in fig. 4, and it can be seen from fig. 4 that the tracking error of the mechanical arm system is limited within a symmetrical time-varying constraint range, so as to ensure that the constraint condition is not violated in the whole process when the mechanical arm system is in a full state.
A state simulation diagram of the arm system is shown in fig. 5, and it can be seen from fig. 5 that the arm system output can quickly and accurately track the reference signal.
Example 2:
the object of this embodiment 2 is to provide a computing apparatus, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and when the processor executes the computer program, the processor implements the following steps, including:
step S1, designing an observer, specifically: establishing a mechanical arm system kinetic equation; establishing an initial state equation of the mechanical arm system; designing a finite time disturbance observer; establishing a state equation of the mechanical arm system;
in step S2, the arm controller is designed based on the back stepping method.
Example 3:
the object of this embodiment 3 is to provide a computer-readable storage medium on which a computer program is stored, which program, when executed by a processor, performs the steps of:
step S1, designing an observer, specifically: establishing a mechanical arm system kinetic equation; establishing an initial state equation of the mechanical arm system; designing a finite time disturbance observer; establishing a state equation of the mechanical arm system;
in step S2, the arm controller is designed based on the back stepping method.
The steps and methods involved in the apparatus of the above embodiment correspond to those of embodiment 1, and the detailed description thereof can be found in the relevant description of embodiment 1. The term "computer-readable storage medium" should be taken to include a single medium or multiple media that include one or more sets of instructions: it should also be understood to include any medium that is capable of storing, encoding or carrying a set of instructions for execution by a processor and that cause the processor to perform any of the methods of the present invention.
The features of the embodiments and embodiments described herein above may be combined with each other without conflict.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (6)

1. A design method of a rapid finite time controller of a full-state constraint mechanical arm is characterized by comprising the following steps:
s1, designing an observer, specifically: establishing a mechanical arm system kinetic equation; establishing an initial state equation of the mechanical arm system; designing a finite time disturbance observer; establishing a state equation of the mechanical arm system;
and S2, designing the mechanical arm controller based on the backstepping method.
2. The method for designing the fast finite-time controller of the all-state constraint mechanical arm according to claim 1, wherein in the step S1, the specific steps of designing the observer are as follows:
s1.1, establishing a mechanical arm system kinetic equation:
Figure FDA0002954683130000011
wherein, q is the angular position,
Figure FDA0002954683130000012
is angular acceleration, M is moment of inertia, M is link mass, g is gravitational acceleration, F is acting force, l is link length;
s1.2, establishing an initial state equation of the mechanical arm system:
the state variables and the control input quantities of the mechanical arm system are defined as follows:
Figure FDA0002954683130000013
wherein x is1、x2Is a state variable of the arm system, u is a control input amount of the arm system,
Figure FDA0002954683130000014
is the angular velocity;
the mechanical arm system dynamics equation (1) is expressed as:
Figure FDA0002954683130000015
wherein d is1And d2Respectively external disturbances; phi1＝0,Φ2(x1)＝-0.5mgl sin(x1)；
S1.3, designing a finite time disturbance observer:
Figure FDA0002954683130000021
wherein v is0i，v1i，v2iAre respectively the intermediate variable, λ0,λ1,λ2Respectively, of a finite-time disturbance observer, σ0i,σ1i,σ2iAre each xi,di,
Figure FDA0002954683130000028
Of the observed value of (A), L1、L2、L3Is an observation coefficient;
s1.4, establishing a state equation of the mechanical arm system:
defining an external disturbance diObserved value of
Figure FDA0002954683130000022
The initial state equation (3) of the mechanical arm system is expressed as:
Figure FDA0002954683130000023
3. the method for designing a fast finite-time controller of a full-state constraint mechanical arm according to claim 2, wherein in step S2, the specific steps for designing the mechanical arm controller based on the backstepping method are as follows:
s2.1, based on disorders plusThe power integration technology selects a Lyapunov function V meeting constraint conditions1：
Figure FDA0002954683130000024
Wherein ξ1Is the tracking error, ξ1＝x1-yd，ydIs a reference signal, η1(t) is a symmetric time-varying constraint function,
Figure FDA0002954683130000025
η11＞η12＞0，η11,η12respectively, constant, t time, τ1Is a time constant;
s2.2, for Lyapunov function V1Calculating the first derivative, simplifying, and selecting proper virtual control law alpha1：
Figure FDA0002954683130000026
Wherein the content of the first and second substances,
Figure FDA0002954683130000029
r2to a selected constant, r2δ is a fraction where both the numerator and denominator are odd and 1/2<δ<1；
Figure FDA0002954683130000027
Is d1The observed value of (a);
s2.3, the design of the virtual control law is combined, and the Lyapunov function V can be guaranteed1Derivative of (2)
Figure FDA0002954683130000031
Wherein a and b respectively represent constants, a is more than 0, and b is more than 0;
s2.4, introducing coordinate transformation:
Figure FDA0002954683130000032
s2.5, selecting a proper Lyapunov function V2：
Figure FDA0002954683130000033
Wherein the content of the first and second substances,
Figure FDA0002954683130000034
η2(t) is a time-varying constraint function,
Figure FDA0002954683130000035
η21＞η22＞0，η21,η22respectively, constant, t time, τ2Is a time constant;
s2.6, for Lyapunov function V2Derivation and simplification, selection of fuzzy logic versus unknown nonlinear functions
Figure FDA0002954683130000036
Performing approximate estimation, non-linear function
Figure FDA0002954683130000037
The expression of (a) is:
Figure FDA0002954683130000038
wherein θ ═ θ1,θ2…,θN]TIs a weight vector, S (x) S1(x),S2(x),…SN(x)]TAnd is and
Figure FDA0002954683130000039
wherein k is 1,2, …, N, j is 1,2, …, N, N and N are natural numbers greater than 1，
Figure FDA00029546831300000310
Is a Gaussian relation function;
s2.7, for non-linear functions
Figure FDA00029546831300000311
Making an identity change to obtain an expression:
y(x)＝θ*TS(x)＋ε(x) (12)
wherein, theta*And ε (x) is the ideal optimal weight and the approximation error under that optimal weight, respectively;
s2.8, using expressions (11) and (12) to apply fuzzy logic to nonlinear function in design process
Figure FDA00029546831300000312
Carrying out approximation processing, thereby designing a fuzzy virtual control law u:
Figure FDA00029546831300000313
wherein the content of the first and second substances,
Figure FDA00029546831300000316
r3k is a selected constant;
Figure FDA00029546831300000314
is d2The observed value of (a);
Figure FDA00029546831300000315
s2.9, the design of the fuzzy virtual control law can ensure the Lyapunov function V2Derivative of (2)
Figure FDA0002954683130000041
Wherein c and d respectively represent constants, c is more than 0, and d is more than 0.
4. A robot arm system comprising a controller, wherein the controller is designed using the design method of any one of claims 1 to 3.
5. A computing device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor when executing the program performs steps comprising:
s1, designing an observer, specifically: establishing a mechanical arm system kinetic equation; establishing an initial state equation of the mechanical arm system; designing a finite time disturbance observer; establishing a state equation of the mechanical arm system;
and S2, designing the mechanical arm controller based on the backstepping method.
6. A computer-readable storage medium, on which a computer program is stored, which program, when executed by a processor, performs the steps of:
s1, designing an observer, specifically: establishing a mechanical arm system kinetic equation; establishing an initial state equation of the mechanical arm system; designing a finite time disturbance observer; establishing a state equation of the mechanical arm system;
and S2, designing the mechanical arm controller based on the backstepping method.
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